CLEVELAND -- Corey Kluber breezed through Chicago's order the second time on Sunday, pitching himself into the Tribe's record books.

Starting with the second out in the top of the third and ending with the second out of the fifth, Kluber fanned seven straight White Sox hitters, setting a new Indians record for consecutive strikeouts. He struck out the first six swinging.

Kluber's gem was for naught after John Axford allowed a three-run homer to Dayan Viciedo in the ninth, but Kluber's records survive the tough 4-3 Tribe loss.

Kluber's key to success was what he did all afternoon, aggressively make good pitches.

"It was kind of the same thing as the whole game, maybe I just happened to get them looking for something else in those at-bats," Kluber said.

By the time he checked out after the eighth, Kluber had a career-high 13 strikeouts. Having struck out 11 in his previous home start, Kluber became the first Indians pitcher to record 11 strikeouts in consecutive home starts since Dennis Eckersley did so in August 1976.

Kluber went eight innings, allowing a run on Jose Abreu's solo homer. Kluber scattered three hits and walked two.

"That ball Abreu hit in the first inning was a good pitch, but he just made an adjustment," Indians manager Terry Francona said.

Breaking the consecutive strikeout record helped Kluber move through the middle innings quickly.

Four Indians pitchers were tied with the previous record, six consecutive strikeouts. Bob Feller, Bartolo Colon, Chuck Finley, and Mitch Talbot each accomplished the feat.

"I think Mickey [Callaway] told me that when I was done," Kluber said of setting the record. "It's pretty cool to be mentioned in the same sentence as Bob Feller, but otherwise, it's just a nice byproduct of having a good game."

Leury Garcia worked Kluber to a full count in the fifth, drawing a walk to end the streak. Kluber followed it up with another strikeout to end the inning.

Stephen Ellsesser is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.